$h(t) = -4t^{2}-7t-4(g(t))$ $g(n) = -n^{2}-4$ $f(t) = 2t^{3}-t^{2}-5(h(t))$ $ h(g(7)) = {?} $
Explanation: First, let's solve for the value of the inner function, $g(7)$ . Then we'll know what to plug into the outer function. $g(7) = -7^{2}-4$ $g(7) = -53$ Now we know that $g(7) = -53$ . Let's solve for $h(g(7))$ , which is $h(-53)$ $h(-53) = -4(-53)^{2}+(-7)(-53)-4(g(-53))$ To solve for the value of $h$ , we need to solve for the value of $g(-53)$ $g(-53) = -(-53)^{2}-4$ $g(-53) = -2813$ That means $h(-53) = -4(-53)^{2}+(-7)(-53)+(-4)(-2813)$ $h(-53) = 387$